Enzo Costanza, 38, was detained by Spanish police on Friday near the city of Albacete and his 16-day-old son taken into care after a three-day man hunt.
Spain's National Police described father and son as being in a "good state" of health. The alert had been raised amid fears that he might be suffering mental health problems.
He had dropped his wife off at the local toyshop near their home in Orbassano near Turin, on Tuesday and said he would remain in the car with the couple’s two-week old son.
But when she returned to the car park after purchasing a toy for her newborn child he had driven away and would not answer his mobile telephone.
She raised the alarm and police used a geotracking in Costanza’s iphone to discover that he had driven over the border into France.
Italy’s Carabineri alerted their French and Spanish counterparts to help in the search.
Witnesses reported having seen him at a hotel in Leon, France where he spent the night and that the baby appeared well cared for.
Costanza’s vehicle, a Fiat Freemont, was spotted later on CCTV in Spain.
On Thursday afternoon he stopped at a petrol station in Cuidad Real and is thought to be attempting to reach Portugal.
His wife, Stefania, 32, told the police that police that Costanza was under the care of a psychiatrist and suffered from “paranoia” but on Tuesday morning after a visit to the doctor had decided to cease taking the medicine prescribed, according to a report in Europa Press.
"My husband has never attempted suicide nor mentioned that he intended to," she said, according to Europa Press. "He has never been violent and always been loving and protective towards the our child," she reportedly said.
Police warn the public that he should not be approached as he could be "unpredicable" but to contact police if spotted.